# Use replicator dynamics with mutationΒΆ

Given a matrix \(Q\) such that \(Q_{ij}\) gives the probability that an individual of type i mutates to an individual of type j, the replicator dynamics equation with mutation can be solved using the following:

```
>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[3, 2], [4, 2]])
>>> Q = np.array([[9 / 10, 1 / 10], [1 / 5, 4 / 5]])
>>> game = nash.Game(A)
>>> game.replicator_dynamics(mutation_matrix=Q)
array([[0.5 , 0.5 ],
[0.50049813, 0.49950187],
[0.50099155, 0.49900845],
...,
[0.55278206, 0.44721794],
[0.5527821 , 0.4472179 ],
[0.55278214, 0.44721786]])
```